Volume III changes the level of analysis. Volumes I and II analysed capital "in general" — the production and circulation of surplus-value in their inner constitution. Volume III follows capital out to the surface of society, into the forms in which it appears to the agents of production themselves and acts through competition: profit, the general rate of profit, interest, rent. The governing thesis of the whole volume is that these surface forms systematically disguise the depths that produced them, so that the origin of surplus-value in unpaid labour becomes ever more thoroughly veiled the closer one gets to the categories of everyday economic consciousness. Part One takes the first step of this descent. It shows how surplus-value assumes the form of profit and how the rate of surplus-value assumes the form of the rate of profit — two transformations that, in one stroke, hide the source of the surplus in the variable capital by referring it instead to the total capital advanced. The cost-price category (k = c + v) obliterates the distinction between constant and variable capital on which the whole theory of exploitation rests; profit (the surplus reckoned against the whole outlay) then appears as an offspring of capital as such rather than of living labour. Chapters 1 through 3 establish the two transformations and the relation between the rates; Chapters 4 through 7 examine how turnover, economies in the use of constant capital, and price fluctuations modify the rate of profit — all of them further loosening the visible tie between profit and its real source.

Marx introduces the cost price, the sum the capitalist actually lays out — constant capital plus variable capital, k = c + v. Because the surplus labour costs the capitalist nothing, the value of the commodity C = c + v + s can be rewritten from his standpoint as k + s, and the surplus, reckoned now against the whole outlay, presents itself as profit. The value-formula becomes the profit-formula, and in the passage the source of the surplus is lost.

Marx fixes the category at the outset: what the commodity costs the capitalist and what its production really costs are two different magnitudes.

When we combine the various portions of commodity value that simply replace the capital value spent in the commodity’s production, under the heading of cost price, we express on the one hand the specific character of capitalist production. The capitalist cost of the commodity is measured by the expenditure of capital, whereas the actual cost of the commodity is measured by the expenditure of labour..

Marx, Capital III, page 118.

And he warns at once that the category, though it explains nothing about the production of value, will nonetheless come to pose as one of its real determinants.

If I know that five-sixths of a commodity value of £600, i.e. £500, is simply an equivalent, a replacement value, for the capital of £500 that has been spent, and that this is therefore just sufficient to buy back, the material elements of this capital, I still neither know how this five-sixths of the commodity’s value which forms its cost price was produced, nor can I explain the origin of the last sixth that forms its surplus-value. Our investigation will show, however, that cost price does none the less, in the economy of capital, present the false semblance of an actual category of value production..

Marx, Capital III, page 119.

Because the surplus appears indifferent to the internal division of the advance, it presents itself as sprung from the capital as a whole — the step by which surplus-value takes on the profit form.